A New Approach to Nonconvex Risk-Sensitive Stochastic Optimization

本奖项的研究目标是开发一个新的框架，将风险纳入不确定性下的顺序决策。该方法的两大支柱是累积前景理论和动态风险度量。该框架建立在这两个研究流的基础上，以形成一个单一的理论，将人类行为的主观偏好与规范性决策目标相结合。现有的基于效用的动态模型无法处理前景理论行为模型所隐含的非凸性，而该框架允许将累积前景理论中的概率加权与传统期望效用公式中常见的结果加权相结合，形成包含两种风险敏感性的序列决策模型。该框架将用于为风险敏感优化和控制问题开发有效的动态规划采样和基于仿真的方法，并研究风险敏感性的新建模如何影响决策者的行为。如果成功，本研究的结果将为目前现有方法的风险决策提供另一种框架。该框架将主要来自心理学和行为经济学的前景理论的主要描述性研究流与通常与微观经济学和运筹学社区相关的规范方法结合起来。这种新方法带来了许多理论和计算上的挑战。将开发算法，用于解决各种应用领域中出现的实际操作和战术决策问题，从制造和供应链管理到服务系统，包括医疗保健、运输和金融工程。

The research objective of this award is to develop a new framework for incorporating risk into sequential decision making under uncertainty. The two pillars of the approach are cumulative prospect theory and dynamic risk measures. The framework builds on both of these research streams to formulate a single theory that integrates subjective preferences in human behavior with normative decision-making objectives. Existing utility-based dynamic models cannot handle the nonconvexity implied by the behavioral models of prospect theory, whereas the framework allows the probability weighting found in cumulative prospect theory to be combined with the usual outcome weighting of traditional expected utility formulations in a sequential decision-making model that incorporates both types of risk sensitivity. The framework will be used to develop efficient dynamic programming sampling and simulation-based methods for risk-sensitive optimization and control problems, and to investigate how the new modeling of risk-sensitivity affects the behavior of decision makers.If successful, the results of this research will provide an alternative framework for decision making under risk to currently existing approaches. The framework unifies the predominantly descriptive research stream of prospect theory coming primarily from psychology and behavioral economics with the normative approaches generally associated with the microeconomics and operations research communities. From this new approach arise a host of challenges, both theoretical and computational. Algorithms will be developed that can be used to address practical operational and tactical decision-making problems arising in a wide variety of application areas, from manufacturing and supply chain management to service systems, including health care, transportation, and financial engineering.